A non-uniform rod $AB$, of length $0.6{\text{ }}m$ and weight $9{\text{ }}N$, has its centre of mass $0.4{\text{ }}m$ from $A$. The end $A$ of the rod is in contact with a rough vertical wall. The rod is held in equilibrium, perpendicular to the wall, by means of a light string attached to $B$. The string is inclined at ${30^ \circ }$ to the horizontal. The tension in the string is $T{\text{ }}N$ (see diagram).
a) Calculate $T$.
b) Find the least possible value of the coefficient of friction at $A$.

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